- #1
Jbreezy
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Homework Statement
Say that you were using ration test for
##
\sum_{n=1}^\infty\frac{(-1)^{n+1} (x-4)^n}{n9^n!}\
##
Homework Equations
The Attempt at a Solution
You take the limit of the above you will get
##\frac {1}{9} |x-4|##
Book says radius of convergence is 9? Is this done by using the ratio test and making an inequality?
##\frac {1}{9} |x-4| <1##
##|x-4| < 9##
No?
OK then the book says in the next line the
##-5< x< 13##
How did they get this? I thought that they maybe said if R = 9 then put ,-9 and 9 in the inequality. So,
##|(-9)-4| = -13## and ## |(9)-4| = 5##
But that doesn't work because it is backwards theirs was -5 and 13 not 13 and -5
What is going on. If you can elaborate the idea of radius of convergence and how they determined the interval please!